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Linear Algebra

Homework 7 - Rank and Nullity

Due 2021-10-12.

  1. Find the nullity and rank of the matrix \(A = \begin{pmatrix} 8 & -1 & 3 & 3 \\ 3 & 0 & 1 & -1 \\ 2 & -1 & 1 & 5 \end{pmatrix}\)

  2. Find the rank and nullity of $A^T$.

  3. Suppose we have $A = BC$. Show that \(\operatorname{rank} A \leq \operatorname{rank} B\)